Let $\mathcal {C} $ be a finite tensor category, and let $\mathcal {M} $ be an exact left
$\mathcal {C} $-module category. The relative Serre functor of $\mathcal {M} $ is an …

We show that indecomposable exact module categories over the category RepH of
representations of a finite-dimensional Hopf algebra H are classified by left comodule …

Let C be a finite tensor category and M an exact left C-module category. We call M
unimodular if the finite multitensor category Rex C (M) of right exact C-module endofunctors …

Let C be a finite tensor category with simple unit object, let Z (C) denote its monoidal center,
and let L and R be a left adjoint and a right adjoint of the forgetful functor U: Z (C)→ C. We …

A Hopf monad is a monad on a tensor category, equipped with comparison maps relating
the monad structure to the tensor structure. We study some general properties of such Hopf …

The categories of representations of finite dimensional quasi-Hopf algebras [Dri90] and
weak Hopf algebras [BNS99] are finite multi-tensor categories. In this thesis I classify exact …

We introduce the notions of normal tensor functor and exact sequence of tensor categories.
We show that exact sequences of tensor categories generalize strictly exact sequences of …

Let A be a ring and MA the category of right A-modules. It is well known in module theory
that any A-bimodule B is an A-ring if and only if the functor−⊗ AB: MA→ MA is a monad (or …

By means of a certain module V and its tensor powers in a finite tensor category, we study a
question of whether the depth of a Hopf subalgebra R of a finite-dimensional Hopf algebra H …

We show that every modular category is equivalent as an additive ribbon category to the
category of finite-dimensional comodules of a Weak Hopf Algebra. This Weak Hopf Algebra …